Why is it necessary to follow the order of operation?

Question

Why is it necessary to follow "order of operation" ?
Please use examples to explain why!
Thanks in advance to anyone who actually tries to help!
Like:
5 x 2 + (6 - 7) + 16
Just explain any problem and tell why it is necessary to follow the order of operation to get a correct answer.
Brackets ()
Exponents
Division
Multiplication
Addition
Subtraction
Solution

Answer 1

Well..... The trivial answer to your question is, "To get the correct answer." But it actually goes a bit deeper than that. If you think about multiplication, it's really just repeated addition. And exponentiation is repeated multiplication. If you think about that long enough, it makes sense that you do the most 'grouped' operations first. The other item is that the 'standard' order of operations is the one that everybody uses and you have to follow them so everybody is 'speaking the same language'.
The safest rule is, when in doubt, put parenthesis around it ☺

Doug

Answer 2

Using your example of 5 x 2 + (6 - 7) + 16 doesn't help, because in this case the left to right order happens to be the same answer as the correct, BEDMASS answer.

Left to Right:

5 x 2 = 10
10 + 6 = 16
16 - 7 = 9
9 + 16 = 25

BEDMASS:

(6 - 7) = -1 therefore 5 x 2 - 1 + 16
5 x 2 = 10 therefore 10 - 1 + 16
- 1 + 16 = 15 therefore 10 + 15
10 + 15 = 25.

But lets move the brackets so the example is 5 x (2 + 6) - 7 + 16.

Left to right you'd still get the same answer since it's still the same order left to right...

with BEDMASS,

2 x 6 = 12 therefore 5 x 12 - 7 +16
5 x 12 = 60 therefore 60 - 7 + 16
-7 + 16 = 9 therefore 60 - 9
60 - 9 = 51. Quite a different answer.....

Answer 3

You see, for example, the problem 3 + 2 X 8 - (4 + 3) , using the correct order, the steps would be:
3 + 2 X 8 - (4 + 3)
= 3 + 16 - 7
= 19 - 7
= 12
(which is correct)

However if you just do it from left to right, ignoring the order, it would be:
3 + 2 X 8 - (4 + 3)
= 5 X 8 - 4 + 3
= 40 - 4 + 3
= 36 + 3
= 39
(which is wrong)

So you see, the answers are very different.

Here are more websites with more examples:
http://www.mathsisfun.com/operation-order-bodmas.html
http://www.easymaths.com/What_on_earth_is_Bodmas.htm
http://www.abacustraining.biz/AboutBodmas.htm

Alternatively, just google 'BODMAS'.

Answer 4

The simplest answer would be that if you DONT follow the order of operation, you will get the wrong answer. The better answer is that the order of operation insures that you correctly apply the properties of division, mult, add & subtract. For example, if you decide in the problem above to add 2+6 and then multiply the result by 5, you will get 40 instead of the correct answer 10.

Answer 5

"Order of operation" is a standard or convention adapted so that everyone will get the same exact answer when faced with a series of arithmetic operations to perform.

A simple example:

What is 5 x 2 + 2?
Is it (5x2) + 2 = 10+2=12?
Or is it 5 x (2+2) = 5 x 4 = 20?

Well, the order of operations standardizes such things so there is no question about what we mean.

Answer 6

It is necessary for all mathematicians to follow the same rules in order to make math be a consistent science.

For example, if 3 + 4*3 is solved from left to right, the answer is 7*3 = 21, but if we solve by multiplying first, the answer is
3+12 = 15. In order to avoid inconsistency, mathematicians long ago decided to multiply first, so the correct answer is 15.

Answer 7

if you don't follow the order of operations, then the answer you get will be wrong. for example, 5+3-4(2)= 0,but,
if you didn't follow the order of operations, then you would get 8.

Answer 8

I actual don't understand WHY we'd want to keep on with it, besides the undeniable fact that this is only the " perfect way " to get an answer. the answer is faulty in case you do not keep on with the order or operations. for instance: first is brackets so do 6-7 ( -a million ) 2d is exponents, yet you've not any 0.33 is branch, you've not any fourth is multiplication so do 5x2 ( 10 ) fifth is addition so do 10 + -a million + 16